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Integers, ratios and percentages

1. Orders, adds and subtracts positive and negative integersBuilds on: Places numbers up to 100 on a number line (Years 1–2); Subtracts two-digit numbers with and without regrouping (Years 1–2)
2. Applies the order of operations to whole-number calculationsBuilds on: Multiplies two- and three-digit numbers by a one-digit number (Years 3–4); Divides two- and three-digit numbers by a one-digit number, with remainders (Years 3–4)
3. Simplifies ratios and divides a quantity in a given ratioBuilds on: Finds equivalent fractions using models and multiplication (Years 5–6); Divides two- and three-digit numbers by a one-digit number, with remainders (Years 3–4)
4. Calculates a percentage of a quantity, including discountsBuilds on: Converts between fractions, decimals and percentages (Years 5–6); Adds, subtracts and multiplies decimals (Years 5–6)
5. Multiplies and divides integers, including with the order of operationsBuilds on: Orders, adds and subtracts positive and negative integers; Applies the order of operations to whole-number calculations
6. Uses rates to compare quantities, including best buys and speedBuilds on: Simplifies ratios and divides a quantity in a given ratio; Divides decimals by whole numbers and by decimals
7. Interprets distance–time graphsBuilds on: Uses rates to compare quantities, including best buys and speed; Plots and reads points in all four quadrants of the Cartesian plane (Years 5–6)

Algebraic techniques and linear equations

1. Describes number patterns and writes the ruleBuilds on: Recalls multiplication facts to 10 × 10 (Years 3–4)
2. Uses algebraic notation with pronumeralsBuilds on: Describes number patterns and writes the rule; Applies the order of operations to whole-number calculations
3. Simplifies algebraic expressions by collecting like termsBuilds on: Uses algebraic notation with pronumerals
4. Solves one-step linear equationsBuilds on: Uses algebraic notation with pronumerals; Orders, adds and subtracts positive and negative integers
5. Plots straight-line graphs from a table of valuesBuilds on: Uses algebraic notation with pronumerals; Plots and reads points in all four quadrants of the Cartesian plane (Years 5–6)
6. Substitutes values into algebraic expressions and formulasBuilds on: Uses algebraic notation with pronumerals; Orders, adds and subtracts positive and negative integers
7. Expands expressions with brackets using the distributive lawBuilds on: Simplifies algebraic expressions by collecting like terms
8. Finds the gradient and y-intercept and writes the equation of a lineBuilds on: Plots straight-line graphs from a table of values
9. Solves quadratic equations of the form ax² = cBuilds on: Solves one-step linear equations; Calculates squares, cubes, square roots and cube roots
10. Solves two-step linear equations, including with bracketsBuilds on: Solves one-step linear equations; Expands expressions with brackets using the distributive law
11. Factorises algebraic expressions using the highest common factorBuilds on: Expands expressions with brackets using the distributive law
12. Solves linear equations graphically using the point of intersectionBuilds on: Plots straight-line graphs from a table of values; Solves two-step linear equations, including with brackets

Fractions, decimals and percentages (Stage 4)

1. Multiplies and divides fractions and mixed numeralsBuilds on: Finds equivalent fractions using models and multiplication (Years 5–6); Multiplies two- and three-digit numbers by a one-digit number (Years 3–4)
2. Divides decimals by whole numbers and by decimalsBuilds on: Adds, subtracts and multiplies decimals (Years 5–6); Divides two- and three-digit numbers by a one-digit number, with remainders (Years 3–4)
3. Expresses one quantity as a fraction or percentage of anotherBuilds on: Converts between fractions, decimals and percentages (Years 5–6); Calculates a percentage of a quantity, including discounts
4. Calculates percentage increase and decrease, including GSTBuilds on: Calculates a percentage of a quantity, including discounts

Primes and indices

1. Expresses whole numbers as products of their prime factorsBuilds on: Recalls multiplication facts to 10 × 10 (Years 3–4); Divides two- and three-digit numbers by a one-digit number, with remainders (Years 3–4)
2. Calculates squares, cubes, square roots and cube rootsBuilds on: Recalls multiplication facts to 10 × 10 (Years 3–4); Expresses whole numbers as products of their prime factors
3. Uses index notation and applies the index laws with numerical basesBuilds on: Expresses whole numbers as products of their prime factors; Calculates squares, cubes, square roots and cube roots

Angle relationships and circles

1. Calculates the circumference and area of circlesBuilds on: Uses formulas to find the area of rectangles and triangles (Years 5–6); Adds, subtracts and multiplies decimals (Years 5–6)
2. Finds the area of composite shapesBuilds on: Uses formulas to find the area of rectangles and triangles (Years 5–6); Calculates the circumference and area of circles
3. Calculates the volume of prisms and cylindersBuilds on: Calculates the volume of rectangular prisms (Years 5–6); Calculates the circumference and area of circles
4. Finds unknown angles using angles at a point, on a line and in trianglesBuilds on: Measures and draws angles with a protractor (Years 5–6); Solves one-step linear equations

Length, area and volume (Stage 4)

1. Calculates perimeters of plane shapes, including composite figuresBuilds on: Calculates the perimeter of rectangles and simple shapes (Years 3–4); Adds, subtracts and multiplies decimals (Years 5–6)
2. Uses formulas to find the area of parallelograms, trapeziums, rhombuses and kitesBuilds on: Uses formulas to find the area of rectangles and triangles (Years 5–6)
3. Calculates the volume and capacity of right prisms with various cross-sectionsBuilds on: Calculates the volume of rectangular prisms (Years 5–6); Uses formulas to find the area of parallelograms, trapeziums, rhombuses and kites

Geometrical figures and parallel lines

1. Classifies triangles and quadrilaterals using their side, angle and symmetry propertiesBuilds on: Measures and draws angles with a protractor (Years 5–6)
2. Uses the angle sum of a quadrilateral to find unknown anglesBuilds on: Finds unknown angles using angles at a point, on a line and in triangles; Classifies triangles and quadrilaterals using their side, angle and symmetry properties
3. Finds unknown angles formed when parallel lines are cut by a transversalBuilds on: Finds unknown angles using angles at a point, on a line and in triangles

Right-angled triangles (Pythagoras)

1. Applies Pythagoras' theorem to find unknown sides in right-angled trianglesBuilds on: Finds unknown angles using angles at a point, on a line and in triangles; Calculates squares, cubes, square roots and cube roots

Probability experiments

1. Calculates theoretical probabilities for single-step experimentsBuilds on: Assigns probabilities to simple events as fractions (Years 5–6); Converts between fractions, decimals and percentages (Years 5–6)
2. Runs experiments and compares relative frequency with theoretical probabilityBuilds on: Calculates theoretical probabilities for single-step experiments
3. Uses tables and tree diagrams for two-step experimentsBuilds on: Calculates theoretical probabilities for single-step experiments
4. Uses complementary events to calculate probabilitiesBuilds on: Calculates theoretical probabilities for single-step experiments

Data classification and analysis

1. Classifies data as categorical or numerical, discrete or continuousBuilds on: Collects data and sorts objects into categories (Years 1–2)
2. Chooses appropriate measures of centre and spread, including the effect of outliersBuilds on: Calculates the mean, median, mode and range of a data set (Years 5–6)
3. Constructs and interprets dot plots and stem-and-leaf plotsBuilds on: Classifies data as categorical or numerical, discrete or continuous; Draws and interprets column graphs (Years 3–4)
4. Constructs frequency tables and histograms for numerical dataBuilds on: Classifies data as categorical or numerical, discrete or continuous; Records data in tables using tally marks (Years 3–4)
5. Describes the shape of data distributions, including symmetry, clusters and outliersBuilds on: Constructs and interprets dot plots and stem-and-leaf plots; Chooses appropriate measures of centre and spread, including the effect of outliers